Mr. Jacobs ignited one of the most contentious backlashes against a developer in recent memory when he proposed a sports campground for 400 children on a 17-acre defunct tennis club. Even for the Hamptons, where year-round residents are known for their fierce protection of privacy and property, the criticism was unusually sharp.

“They had people standing on the streets of Southampton in front of stores and giving out leaflets that said I was a liar,” said Mr. Jacobs, who has filed a libel lawsuit.